https://www.fountain.fm/episode/qTF5i2hYxgbbC0W2lgOl

Bitcoin doesn’t need more believers. It needs more understanders. Come aboard in conversational form - then access the free textbooks and YouTube videos.

Appreciate the clip. Hope people understand the context the way you do. Nothing is given.

The inverse problem in Bitcoin cryptography:

Given P = kG (public key = private key × generator point), finding k is the discrete logarithm problem — computationally infeasible.

But step back: why does k⁻¹ exist at all?

THEOREM: In a finite field 𝔽ₚ where p is prime, every non-zero element a has a multiplicative inverse a⁻¹ such that a × a⁻¹ ≡ 1 (mod p).

PROOF: By Fermat's Little Theorem, a^(p-1) ≡ 1 (mod p) for any a ≠ 0.
Therefore: a × a^(p-2) ≡ 1 (mod p)
So: a⁻¹ = a^(p-2)

This is why Bitcoin works. Not luck — mathematical certainty.

New episode breaks it down: fountain.fm/show/2gdYQCIV0eZEuYOW3nGJ

🔑 Magic Internet Math Episode 4: Why the Inverse Problem Works

Bitcoin's security rests on the inverse problem — but why does an inverse even EXIST?

This isn't "the math is hard." This is PROOF that every non-zero element in a finite field 𝔽ₚ has a multiplicative inverse.

We cover:

Euclidean Algorithm (computing inverses)
Fermat's Little Theorem (a^(p-1) ≡ 1 mod p)
Why secp256k1 uses a prime field
Group & field axioms (closure, identity, inverse)
LibSecP implementation
92 minutes with @Rob Hamilton 📖 Study guide: ecc-study-guide.magicinternetmath.com/guide.pdf
🎧 Listen: fountain.fm/show/2gdYQCIV0eZEuYOW3nGJ

Bitcoin isn't probably secure. It's PROVABLY secure.

⚡ Value-enabled.

I loved this conversation!

Got a new bot - gonna be dropping math knowledge on Nostr.

I’m gonna fix the LaTeX formatting.

Follow it and visit magicinternetmath.com to start leveling up

I just mass-loaded 96 math courses onto Nostr.

High school algebra through elliptic curve cryptography. Euclid's Elements through FROST threshold signatures. Austrian economics through stochastic calculus. 5,000+ interactive sections.
All free. All for Bitcoiners.
Because if you can't explain why Bitcoin uses a 256-bit curve, you don't understand the security model. If you can't follow a Schnorr signature derivation, you're trusting someone else's math. And if you're trusting someone else's math, you're a second-class citizen in Bitcoin.

The bot drops a daily lesson — definitions, theorems, worked examples, the whole thing. Follow it. Zap it when it teaches you something. Mute it if you'd rather stay ignorant.

@MagicInternetMath Bot